The research conclusion of reverse engineering of logarithmic spiral bevel gear is mainly reflected in the following aspects:
1.The tooth surface data points of logarithmic spiral bevel gear are collected by 3D laser scanner, and the collected tooth surface data information is processed by inverse software Imageware. There are about 876011 data points before processing and about 118306 data points after processing, and a more ideal tooth surface point cloud of logarithmic spiral bevel gear is obtained.
2.The basic idea of reconstructing the real tooth surface of logarithmic spiral bevel gear is described. The original data points of the processed tooth surface are inversely calculated by NURBS algorithm, and the profile control points required to construct the tooth surface curve are further formed. The profile control points needed to construct the real tooth surface are calculated back from the formed interpolation curve, and the real tooth surface of logarithmic spiral bevel gear is reconstructed by Imageware. By comparing the real tooth surface with the original point cloud data, it is known that the maximum geometric error of the reconstructed real tooth surface is 0.1533mm, which is less than the standard value of 0.5mm, the average error is 0.1mm, and there is no transverse error, which is within the error range. The results show that the tooth surface of logarithmic spiral bevel gear reconstructed by NURBS algorithm meets the accuracy requirements.
3.Based on the reconstruction of the real tooth surface, the mathematical model of the real tooth surface of logarithmic spiral bevel gear is established and solved. Firstly, the parametric change law of discrete data points of the tooth surface must be determined. For the parameterization of the tooth surface of logarithmic spiral bevel gear, it not only determines the one-to-one correspondence between the points on the tooth surface and the values in the parameter domain, but also controls the shape of the tooth surface. The mathematical model of tooth surface is solved by MATLAB.
4.The errors of real tooth surface and theoretical tooth surface are analyzed. The discrete data points of the real tooth surface are solved by debour recursive algorithm, and compared with the discrete data points of the theoretical tooth surface, the tooth surface normal deviation of the corresponding points is calculated. Through the difference surface analysis tool, the difference surface equation is established and solved.
5.Based on the difference surface equation, the error analysis of the real tooth surface and the theoretical tooth surface is carried out to minimize the distance and direction between the theoretical tooth surface and the real tooth surface, and the expected ideal effect is achieved. For the next step, the contact analysis of the tooth surface of logarithmic spiral bevel gear and the correction of machine tool parameters are carried out, It provides a basis for improving the tooth surface machining quality and machining accuracy of logarithmic spiral bevel gear.